Density-dependent incompressible fluids with non-Newtonian viscosity

F. Guillén-González

Displaying similar documents to “Density-dependent incompressible fluids with non-Newtonian viscosity”

Smoothness properties of solutions to the nonlinear Stokes problem with nonautonomous potentials

Dominic Breit (2013)

Commentationes Mathematicae Universitatis Carolinae

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We discuss regularity results concerning local minimizers $u : ℝ^{n} \supset Ω \to ℝ^{n}$ of variational integrals like $\begin{matrix} \int_{Ω} {F (\cdot, ε (w)) - f \cdot w} d x \end{matrix}$ defined on energy classes of solenoidal fields. For the potential $F$ we assume a $(p, q)$ -elliptic growth condition. In the situation without $x$ -dependence it is known that minimizers are of class $C^{1, α}$ on an open subset $Ω_{0}$ of $Ω$ with full measure if $q < p \frac{n + 2}{n}$ (for $n = 2$ we have $Ω_{0} = Ω$ ). In this article we extend this to the case of nonautonomous integrands. Of course our result extends to weak solutions of the corresponding...

Multiplicity of positive solutions for some quasilinear Dirichlet problems on bounded domains in $ℝ^{n}$

Dimitrios A. Kandilakis, Athanasios N. Lyberopoulos (2003)

Commentationes Mathematicae Universitatis Carolinae

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We show that, under appropriate structure conditions, the quasilinear Dirichlet problem $\{\begin{matrix} - div (| \nabla u |^{p - 2} \nabla u) = f (x, u), & x \in Ω, u = 0, & x \in \partial Ω, \end{matrix}$ where $Ω$ is a bounded domain in $ℝ^{n}$ , $1 < p < + \infty$ , admits two positive solutions $u_{0}$ , $u_{1}$ in $W_{0}^{1, p} (Ω)$ such that $0 < u_{0} \leq u_{1}$ in $Ω$ , while $u_{0}$ is a local minimizer of the associated Euler-Lagrange functional.

Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids

G. Ströhmer, W. Zajączkowski (1999)

Applicationes Mathematicae

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Local existence of solutions is proved for equations describing the motion of a viscous compressible barotropic and self-gravitating fluid in a domain bounded by a free surface. First by the Galerkin method and regularization techniques the existence of solutions of the linearized momentum equations is proved, next by the method of successive approximations local existence to the nonlinear problem is shown.

A plane problem of incompressible magnetohydro-dynamics with viscosity and resistivity depending on the temperature

Giovanni Cimatti (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The plane flow of a fluid obeying the equations of magnetohydrodynamics is studied under the assumption that both the viscosity and the resistivity depend on the temperature. Some results of existence, non-existence, and uniqueness of solution are proved.

Displaying similar documents to “Density-dependent incompressible fluids with non-Newtonian viscosity”

Smoothness properties of solutions to the nonlinear Stokes problem with nonautonomous potentials

Multiplicity of positive solutions for some quasilinear Dirichlet problems on bounded domains in ℝ n

Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids

A plane problem of incompressible magnetohydro-dynamics with viscosity and resistivity depending on the temperature

Multiplicity of positive solutions for some quasilinear Dirichlet problems on bounded domains in $ℝ^{n}$